The three inequalities that define the unshaded region are x ≤ 4, y < x + 3 and y ≥ -2x + 12
What three inequalities define the unshaded region?
From the question, we have the following parameters that can be used in our computation:
The graph
First, we have a vertical line that passes through the point x = 4
The left side of the line is shaded
So, we have
x ≤ 4
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
Calculating the other inequalities, we have
(1)
y = mx + 3
Using other points, we have
2m + 3 = 5
m = 1
So, we have
y = x + 3
Considering the shaded region and the inequality line, we have
y < x + 3
(2)
y = mx + 12
Using other points, we have
3m + 12 = 6
m = -2
So, we have
y = -2x + 12
Considering the shaded region and the inequality line, we have
y ≥ -2x + 12
Hence, the three inequalities are x ≤ 4, y < x + 3 and y ≥ -2x + 12